Traktrisa

diplomsko delo

Nadja Apšner (Avtor), Marko Razpet (Mentor)

Povzetek

V diplomskem delu je predstavljena transcendentna ravninska krivulja traktrisa in njej sorodne krivulje. Na ravnini traktriso opisuje točkasta masa, ki je privezana na neraztegljivi niti konstantne dolžine, katere prosti konec vlečemo po premici v tej ravnini. Običajno je ta premica abscisna os. Namen diplomskega dela je čim bolj temeljita obravnava traktrise. V ta namen so opisane lastnosti le-te ter v povezavi z njo narejeni izračuni ploščine, ločne dolžine, ter površine in prostornine telesa, ki ga dobimo z vrtežem traktrise okoli njene asimptote. Ploskev imenujemo psevdosfera, ki ima konstantno negativno Gaussovo ukrivljenost. Opisan je nastanek traktrise s preprostimi mehanskimi orodji in nastanek modela psevdosfere. Na koncu so predstavljene še traktrisi sorodne krivulje in njihov nastanek.

Ključne besede

koordinatni sistem;ravninske krivulje;psevdosfera;

Podatki

Jezik:	Slovenski jezik
Leto izida:	2016
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[N. Apšner]
UDK:	514.752.2(043.2)
COBISS:	11069257
Št. ogledov:	953
Št. prenosov:	132
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Tractrix
Sekundarni povzetek:	The diploma thesis presents a transcendent plane curve, called tractrix, and its related curves. On the plane the tractrix is defined by a dotted mass that is attached to the tensile nor constant size, the free end is drawn by the straight line in that plane. This is usually a straight line abscissa. The purpose of this diploma thesis is to thoroughly study the tractrix. For this purpose there are basic descriptions of it and in connection also made calculations of the area, arc lenght, area of the surface and volume, which we get with rotating tractrix around it’s asymptote. The surface is called pseudosphere and it has a constant negative Gaussian curvature. Described is also the emergence of the tractrix with simple mechanical tools and the creation of a model of pseudosphere. In conclusion there are being presented different formations of tractrix and also connections with others curves.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo
Komentar na gradivo:	Univ. v Ljubljani, Pedagoška fak., Matematika in Fizika
Strani:	XII, [63] str.
ID:	9154844